A large number of interstellar dust clouds, with various values of visual absorption, was surveyed in the 21-cm line of neutral hydrogen using high-velocity resolution, in a search for narrow absorption lines in the HI emission profiles which could be attributed to the presence of cold HI in the dust clouds. It was found that somewhat less than half of the dust clouds observed were associated with such self-absorption dips and that the greater the observed optical density of the clouds, the greater their chance of showing up in self-absorption. The radial velocities of this group of dust clouds were used to study the kinematics of the local dust cloud population. It was found that the radial velocities of the dust clouds are very close to the Hi peak emission velocities in the same directions, showing that the dust clouds are part of the general local system of interstellar matter. The observations were analyzed using simple models for the density and temperature distribution of the atomic hydrogen in the dust clouds. These calculations showed that the Hi velocities are very close to the OH and H2 CO velocities, and that the mean excitation temperature of the HI in the observed dust clouds ranges from 16 K to 40 K; these are much higher values than those found for the molecules in dust clouds. The calculated central optical depths of the clouds are found to range between about 0.5 and 4.0, and the calculated HI column densities, generally a few times 1020 atom , have only about % of the values predicted from the OH or dust column densities, so that much of the hydrogen in dense interstellar dust clouds must be in some form other than Hi, most probably H2. The line shapes for several of the HI clouds are suggestive of the presence of systematic expansion or contraction motions. or all such clouds, the line shapes are consistent with a model of a contracting cloud slightly hotter at the center, suggesting that the clouds are in a fairly advanced stage of collapse.